CAT 2022 Slot 3 QA Q20 Equations

Question 20 of the Quantitative Ability (QA) section, CAT 2022 Slot 3, with CAT's official answer and a worked solution.

A donation box can receive only cheques of ₹100, ₹250, and ₹500. On one good day, the donation box was found to contain exactly 100 cheques amounting to a total sum of ₹15250. Then, the maximum possible number of cheques of ₹500 that the donation box may have contained, is

TITA: type in the answer. There are no options and no negative marking.

Answer: 12 Equations TITA

Solution

  1. Let counts of ₹100, ₹250, ₹500 cheques be \(a,b,c\): \(a+b+c=100\), \(2a+5b+10c=305\).
  2. Subtract twice the first: \(3b+8c=105\).
  3. \(c\) must be a multiple of 3 and \(8c\le105\Rightarrow c\le13\). So the maximum is \(c=12\), with \(b=3,\ a=85\).

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